Subgroups — D₅×C₁₁×D₃₃ #20300109

Order 7260.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₁₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₁×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₁×D₁₁	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₁×D₃₃	—	5	1	no	maximal, Hall
7	C₁₁×D₅₅	—	3	1	no	—
8	D₅×C₁₁²	D₃	1	1	yes	characteristic, complemented
9	C₅×C₁₁×D₁₁	—	3	1	no	—
10	C₂×C₃×C₁₁²	—	5	1	no	—
11	C₁₁×D₃₃	—	5	1	no	—
12	C₁₁×D₃₃	D₅	1	1	yes	characteristic, direct product factor
13	D₅×D₃₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor
14	D₃×D₅×C₁₁	—	11	1	no	maximal
15	C₅×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁×D₁₁	—	15	1	no	Hall
17	C₃×C₁₁²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	D₁₆₅	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₁₁×D₁₅	—	11	1	no	—
20	C₅×D₃₃	C₂×C₁₁	1	1	yes	characteristic, complemented
21	C₅×D₃×C₁₁	—	11	1	no	—
22	C₃×D₅×C₁₁	—	2	5	no	—
23	C₃×D₅×C₁₁	D₁₁	1	1	yes	characteristic, complemented
24	C₃×D₅×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
25	C₂×C₁₁²	—	5	1	no	—
26	C₁₁×D₁₁	—	3	1	no	—
27	C₁₁×D₁₁	—	15	1	no	—
28	C₂×D₅×C₁₁	—	33	1	no	—
29	D₅×D₁₁	—	3	1	no	—
30	C₃×C₅×C₁₁	—	2	5	no	—
31	C₃×C₅×C₁₁	C₂×D₁₁	1	1	yes	characteristic, complemented
32	C₃×C₅×C₁₁	C₂²×C₁₁	1	1	yes	characteristic, complemented
33	C₂×D₃₃	—	5	1	no	—
34	C₂×D₃×C₁₁	—	55	1	no	—
35	C₁₁²	D₃×D₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₅×C₁₁	—	33	1	no	—
37	D₅₅	—	3	1	no	—
38	C₅×D₁₁	—	3	1	no	—
39	D₅×C₁₁	—	2	5	no	—
40	D₅×C₁₁	—	33	1	no	—
41	D₅×C₁₁	D₃×C₁₁	1	1	yes	characteristic, complemented
42	D₅×C₁₁	D₃₃	1	1	yes	characteristic, direct product factor
43	C₂×C₃×C₁₁	—	5	1	no	—
44	C₂×C₃×C₁₁	—	5	1	no	—
45	C₂×C₃×C₁₁	—	10	5	no	—
46	D₃₃	—	5	1	no	—
47	D₃₃	D₅×C₁₁	1	1	yes	characteristic, direct product factor
48	D₃×C₁₁	—	11	1	no	—
49	D₃×C₁₁	—	55	1	no	—
50	D₃×D₅	—	11	1	no	Hall
51	C₅×C₁₁	—	2	5	no	—
52	C₅×C₁₁	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented
53	C₅×C₁₁	C₂×D₃₃	1	1	yes	characteristic, complemented
54	C₂²×C₁₁	—	165	1	no	—
55	C₂×D₁₁	—	15	1	no	—
56	C₃×C₁₁	—	2	5	no	—
57	C₃×C₁₁	D₅×D₁₁	1	1	yes	characteristic, complemented
58	C₃×C₁₁	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented
59	D₁₅	—	11	1	no	—
60	C₃×D₅	C₁₁×D₁₁	1	1	yes	characteristic, complemented
61	C₅×D₃	—	11	1	no	—
62	C₂×C₁₁	—	5	1	no	—
63	C₂×C₁₁	—	5	1	no	—
64	C₂×C₁₁	—	10	5	no	—
65	C₂×C₁₁	—	33	1	no	—
66	C₂×C₁₁	—	165	1	no	—
67	D₁₁	—	3	1	no	—
68	D₁₁	—	15	1	no	—
69	C₂×D₅	—	33	1	no	Hall
70	C₃×C₅	C₂×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
71	C₂×D₃	—	55	1	no	Hall
72	C₁₁	—	2	5	no	—
73	C₁₁	D₃×D₅×C₁₁	1	1	yes	characteristic, complemented
74	C₁₁	D₅×D₃₃	1	1	yes	characteristic, direct product factor
75	C₂×C₅	—	33	1	no	—
76	D₅	—	33	1	no	—
77	D₅	C₁₁×D₃₃	1	1	yes	characteristic, direct product factor
78	C₂×C₃	—	5	1	no	—
79	D₃	—	11	1	no	—
80	D₃	—	55	1	no	—
81	C₅	C₂×C₁₁×D₃₃	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	165	1	no	Sylow
83	C₃	D₅×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	5	1	no	—
85	C₂	—	33	1	no	—
86	C₂	—	165	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₅×D₃₃
commutator, hypocenter	C₃×C₅×C₁₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁²	C₂²
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₁₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₁×D₁₆₅	C₂	semidirect
2. C₅×C₁₁×D₃₃	C₂	semidirect
3. C₃×D₅×C₁₁²	C₂	semidirect
5. C₃×C₅×C₁₁²	C₂²	semidirect
8. D₅×C₁₁²	D₃	semidirect
12. C₁₁×D₃₃	D₅	direct (N × H)
13. D₅×D₃₃	C₁₁	direct (N × H)
15. C₅×C₁₁²	C₂×D₃	semidirect
17. C₃×C₁₁²	C₂×D₅	semidirect
18. D₁₆₅	C₂×C₁₁	semidirect
20. C₅×D₃₃	C₂×C₁₁	semidirect
23. C₃×D₅×C₁₁	D₁₁	semidirect
24. C₃×D₅×C₁₁	C₂×C₁₁	semidirect
31. C₃×C₅×C₁₁	C₂×D₁₁	semidirect
32. C₃×C₅×C₁₁	C₂²×C₁₁	semidirect
35. C₁₁²	D₃×D₅	semidirect
41. D₅×C₁₁	D₃×C₁₁	semidirect
42. D₅×C₁₁	D₃₃	direct (N × H)
47. D₃₃	D₅×C₁₁	direct (N × H)
52. C₅×C₁₁	C₂×D₃×C₁₁	semidirect
53. C₅×C₁₁	C₂×D₃₃	semidirect
57. C₃×C₁₁	D₅×D₁₁	semidirect
58. C₃×C₁₁	C₂×D₅×C₁₁	semidirect
60. C₃×D₅	C₁₁×D₁₁	semidirect
70. C₃×C₅	C₂×C₁₁×D₁₁	semidirect
73. C₁₁	D₃×D₅×C₁₁	semidirect
74. C₁₁	D₅×D₃₃	direct (N × H)
77. D₅	C₁₁×D₃₃	direct (N × H)
81. C₅	C₂×C₁₁×D₃₃	semidirect
83. C₃	D₅×C₁₁×D₁₁	semidirect

Subgroups — D5×C11×D33 #20300109

Conjugacy classes of subgroups

Complements

Subgroups — D₅×C₁₁×D₃₃ #20300109